Question

Define modulation index. Why is it's value kept, in practice, less than one?
A carrier wave of frequency 1.5 MHz and amplitude 50 V is modulated by a sinusoidal wave of frequency 10 kHz producing 50% amplitude modulation. Calculate the amplitude of the AM wave and frequencies of the side bands produced.

Answer 1

The modulation index $\mu$, can be defined as the ratio between the amplitude of the modulating signal and the amplitude of the carrier signal.
A modulation index above 1 causes over-modulation, resulting in distorted waveform envelope which will result in distorted output signal.

Given, carrier wave frequency = 1.5 MHz,
carrier wave amplitude, $V_c=50V$
Sinusoidal wave frequency = 10 kHz
Amplitude modulation = 50%

Now, Modulation factor $=\frac{50}{100}=0.5$

and $0.5=\frac{V_m}{V_c}$

$0.5=\frac{V_m}{50}$

$V_m=0.5\times 50=25V$

Thus, amplitude of the AM wave = 25 volt

Now, $f_{USB}=1.5\times 1000+10$

$=1500+10=1510kHz$

$f_{LSB}=1.5\times 1000-10=1490kHz$